PeopleofSuperintelligence

Researcher

Mufan Li

Also known as Mufan Bill Li, Bill Li

Mufan Li is a deep learning theorist who studies how neural networks behave when their depth and width grow together. He studied for a PhD in the Department of Statistical Sciences at the University of Toronto from 2017 to 2023, advised by Daniel Roy and Murat Erdogdu. With Mihai Nica and Roy, he described ReLU ResNets at initialization with a log-Gaussian limit in 2021 and the Neural Covariance SDE in 2022, and he coauthored The Shaped Transformer in 2023. From 2023 to 2025, he was a DataX Postdoctoral Research Associate at Princeton University, where he worked with Boris Hanin and took part in the 2025 CompleteP paper on compute-efficient deep transformers. Since July 2025, he is an Assistant Professor in the Department of Statistics and Actuarial Science at the University of Waterloo and a Faculty Affiliate at the Vector Institute.

Timeline

  1. 2017–2023

    PhD in statistical sciences

    He studies for a PhD in the Department of Statistical Sciences at the University of Toronto from 2017 to 2023, advised by Daniel Roy and Murat Erdogdu. In Fall 2021, he is a visiting graduate student at the Simons Institute for the Theory of Computing in its Geometric Methods in Optimization and Sampling program.

  2. 2021

    Log-Gaussian ResNets

    In June 2021, he posts The Future is Log-Gaussian with Mihai Nica and Daniel Roy, which shows that ReLU ResNets at initialization follow a log-Gaussian limit when depth and width grow together. The paper appears at NeurIPS 2021, and he receives a Student Research Presentation Award at SSC 2021.

  3. 2022

    The Neural Covariance SDE

    In June 2022, he posts The Neural Covariance SDE with Mihai Nica and Daniel Roy, which shows that the random covariance matrix of a shaped network at initialization follows a stochastic differential equation in the infinite depth-and-width limit. The paper is an oral at NeurIPS 2022.

  4. 2023

    The Shaped Transformer

    In 2023, he coauthors The Shaped Transformer with Lorenzo Noci, Chuning Li, Bobby He, Thomas Hofmann, Chris Maddison and Daniel Roy. The paper describes a modified softmax attention model with skip connections in the infinite depth-and-width limit through a stochastic differential equation, and it appears at NeurIPS 2023.

  5. 2023–2025

    Postdoc at Princeton

    From 2023 to 2025, he is a DataX Postdoctoral Research Associate at Princeton University, where he works with Boris Hanin.

  6. 2024

    Scaling limits and hyperparameter transfer

    In 2024, he publishes Differential Equation Scaling Limits of Shaped and Unshaped Neural Networks with Mihai Nica in TMLR, which connects shaped and unshaped network architectures. The ICLR 2024 paper Depthwise Hyperparameter Transfer in Residual Networks, coauthored with Blake Bordelon, Lorenzo Noci, Boris Hanin and Cengiz Pehlevan, shows optimal hyperparameters transferring across width and depth.

  7. 2025

    CompleteP for deep transformers

    In May 2025, he is among the authors of Don't be lazy: CompleteP enables compute-efficient deep transformers, with Nolan Dey, Lorenzo Noci, Boris Hanin, Joel Hestness and others. CompleteP is a parameterization that transfers hyperparameters across depth and keeps all layers learning features, and it gives 12–34% compute-efficiency improvements over the prior state of the art; the paper appears at NeurIPS 2025.

  8. Since 2025

    Assistant Professor at Waterloo

    In July 2025, he joins the Department of Statistics and Actuarial Science at the University of Waterloo as an Assistant Professor, and he is a Faculty Affiliate at the Vector Institute. His research focuses on deep learning theory, in particular scaling limits of neural networks, and he teaches STAT 946 Deep Learning Theory in Fall 2025.

Career

  1. Since 2025University of WaterlooAssistant Professor
  2. Since 2025Vector InstituteFaculty Affiliate
  3. 2023–2025Princeton UniversityDataX Postdoctoral Research Associate
  4. 2021Simons Institute for the Theory of ComputingVisiting Graduate Student

Education

  1. 2023University of TorontoPhD

From the biography.

  1. Of 943 people shaping AI who worked at Google, 446 work there nowIncludes Vector Institute. Our estimates of where the 943 people shaping AI who worked at Google and Google DeepMind work now: 446 at Google and 452 across 278 other organizations.
  2. Nonprofit roles are 2.3 times as common in AI safetyIncludes Vector Institute. We estimate where people focused on safety, alignment and evaluation work. Nonprofit roles appear for 25.1% of safety people with known affiliations, compared with 11.0% in other areas.
  3. Universities (31%) and startups and other companies (25%) employ the largest shares of 2020–2026 entrantsIncludes Vector Institute. Among 819 people whose first recorded role started in 2020–2026 and who have a known current organization, 60% work in commercial sectors (25% at startups and other companies, 23% at frontier labs and 13% at big tech, with 9 in two), and 31% work at universities, compared with 66% for earlier entrants.
  4. The United States employs an estimated 48% of people shaping AIIncludes Vector Institute. We estimate where the people shaping AI work today, how universities, companies and research institutes split across countries, and how country shares have changed since the 1960s.

Colleagues

People named in this biography, and people with dated positions at the same organization in the same years.

Sources and credits

Photo: We have no published photo of Mufan Li yet. Send us a free-licensed photo.

  1. Mufan Li mufan-li.github.io. Checked 21 October 2026.
  2. Mufan Li (University of Waterloo): deep learning theory — Lacuna lacuna.tiptreesystems.com. Checked 21 October 2026.
  3. Bill Li | Simons Institute for the Theory of Computing simons.berkeley.edu. Checked 21 October 2026.
  4. The Future is Log-Gaussian: ResNets and Their Infinite-Depth-and-Width Limit at Initialization (arXiv) arxiv.org. Checked 21 October 2026.
  5. Daniel Roy danroy.org. Checked 21 October 2026.
  6. Research - Mufan Li mufan-li.github.io. Checked 21 October 2026.
  7. The Neural Covariance SDE: Shaped Infinite Depth-and-Width Networks at Initialization (arXiv) arxiv.org. Checked 21 October 2026.
  8. The Shaped Transformer: Attention Models in the Infinite Depth-and-Width Limit (arXiv) arxiv.org. Checked 21 October 2026.
  9. Differential Equation Scaling Limits of Shaped and Unshaped Neural Networks (arXiv) arxiv.org. Checked 21 October 2026.
  10. Depthwise Hyperparameter Transfer in Residual Networks: Dynamics and Scaling Limit (arXiv) arxiv.org. Checked 21 October 2026.
  11. Don't be lazy: CompleteP enables compute-efficient deep transformers (arXiv) arxiv.org. Checked 21 October 2026.
  12. Mufan Li | Math Innovation | University of Waterloo uwaterloo.ca. Checked 21 October 2026.
  13. Mufan Li - Vector Institute for Artificial Intelligence vectorinstitute.ai. Checked 21 October 2026.
  14. Teaching - Mufan Li mufan-li.github.io. Checked 21 October 2026.